Systems of linear equations, once again.

Consider a system of linear equations like  1, where the number of rows equals the number of unknowns, i.e. p=n. We can write it in matricial form AX=B, where

• A=a_ij is the coefficient matrix of the system (v.s.  refrestricted matrix)
• B is a matrix of order $n \times 1$, whose single column is identical to the last column of the augmented matrix of the system (v.s.  refaugmented matrix).
• X is the unknown one-column matrix $\begin{pmatrix}x_1 \\ x_2 \\ \dots \\ x_n \end{pmatrix}$.

Suppose that A is invertible. We have:

$AX=B \longleftrightarrow X=A^{-1}B.$